Viewing a single comment thread. View all comments

jimmymvp t1_j6w4ezb wrote

Any application where you need exact likelihoods, flows are king. Such is the case for example jf you're learning a sampling distribution for MCMC sampling, estimating normalizing constants (I believe in physics there are a lot of these problems) etc.

9

badabummbadabing t1_j6wfsok wrote

Exact likelihoods are what attracted me to normalizing flows once, too. But I soon found them too hard to train to yield any useful likelihoods. The bijectivity constraint (meaning that your 'latent' space is just as large as your data space) seems like too much of a restriction in practice. For my application, switching to variational models and just accepting that I'll only get lower bounds on the likelihood got me further in the end. Diffusion models would be a more 'modern' option in this regard as well.

Are you aware of any applications, where people actually use NFs for likelihoods? I am aware of some research papers, but I'd say that their experiments are too much of a contrived example to convince me that this will ever find its way into an actual application.

3

based_goats t1_j6xftq6 wrote

In science/physics flows are the dominant tool for simulation-based inference. The alternative is lengthy rejection sampling. Diffusion-based models are making an entrance in this area as well but are not as well-understood for practitioners to switch.

3

jimmymvp t1_j71bvhf wrote

The problem with diffusion from an SDE view is that you still don't have exact likelihoods because you're again not computing the exact Jacobian to make it tractable and you have ODE solving errors. People mostly resolve to Hutchinson trace estimator, otherwise it would be too expensive to compute, so I don't think that diffusion in this way is going to enter the MCMC world anytime soon.

1

based_goats t1_j72jd9z wrote

There are some papers showing diffusion working better for high-dimensional data in likelihood free inference, even just using an elbo bound. Can dig up later if wanted

1

badabummbadabing t1_j76tfqt wrote

Fully agree from a technical perspective with you.

The difference is that at best, you only get the likelihood under your model of choice. If that happens to be a bad model of reality (which I'd argue is the case more often than not with NFs), you might be better off just using some approximate likelihood (or ELBO) of a more powerful model.

But I am not an expert in MCMC models, so I might be talking out of my depth here. I was mainly using these models for MAP estimation.

1

jimmymvp t1_j7aend6 wrote

Indeed, if your model is bad at modeling the data there's not much use in computing the likelihoods. If you want to just sample images that look cool, you don't care that much about likelihoods. However, there are certain use-cases where we care about exact likelihoods, estimating normalizing constants and providing guarantees for MCMC. Granted, you can always run MCMC with something close to a proposal distribution. However, obtaining nice guarantees on convergence and mixing times (correctness??) is difficult then, I don't know how are you supposed to do this when using a proposal for which you can't evaluate the likelihood. Similarly when you talk about importance sampling, you can only obtain correct weights if you have the correct likelihoods, otherwise it's approximate, not just in the model but also in the estimator.

This is the way I see it at least, but I'll be sure to read the aforementioned paper. I'm also not sure how much having the lower bound hurts you in estimation.

2

jimmymvp t1_j71cgkw wrote

There is a trick how you can get away with gradually expanding your latent dimension with normalising flows, if you assume that the dimensions are independent to a certain point, then you sample from a base distribution and concatenate in the middle of the flow.

Again, MCMC sampling, simulation based inference are examples. Imagine you have an energy function that describes the distribution (you don't have data), how do you sample from this distribution? You would do some MCMC, how would you arrive to a good proposal distribution to make the MCMC algorithm more efficient? You would fit the proposal based on some limited data that you have or inductive biases such as certain invariances etc.

3

PHEEEEELLLLLEEEEP t1_j72txfo wrote

Diffusion models can also generate exact likelihoods so maybe we'll see a shift to those in the future

1

jimmymvp t1_j7aex0t wrote

In theory yes, in practice it's not exact, it's approximated via trace estimator and ODE solver.

1